Average Error: 62.0 → 62.0
Time: 3.5s
Precision: 64
\[lo \lt -1.000000000000000010979063629440455417405 \cdot 10^{308} \land hi \gt 1.000000000000000010979063629440455417405 \cdot 10^{308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{x - lo}{hi - lo}\]
\frac{x - lo}{hi - lo}
↓
\frac{x - lo}{hi - lo}
double f(double lo, double hi, double x) {
        double r13846 = x;
        double r13847 = lo;
        double r13848 = r13846 - r13847;
        double r13849 = hi;
        double r13850 = r13849 - r13847;
        double r13851 = r13848 / r13850;
        return r13851;
}
↓
double f(double lo, double hi, double x) {
        double r13852 = x;
        double r13853 = lo;
        double r13854 = r13852 - r13853;
        double r13855 = hi;
        double r13856 = r13855 - r13853;
        double r13857 = r13854 / r13856;
        return r13857;
}

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo}\]

  2. Final simplification62.0

    \[\leadsto \frac{x - lo}{hi - lo}\]

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e308) (> hi 1e308))
  (/ (- x lo) (- hi lo)))